Evaluation of technical, pure technical and scale efficiencies of Indian banks: An analysis from cross-sectional perspective

Evaluation of technical, pure technical and scale efficiencies of Indian bans: An analysis from cross-sectional perspective A paper submitted for presentation in The 3th Annual Conference on Money and Finance in the Indian Economy on 25-26 th February, 20 Indira Gandhi Institute of Development Research, Mumbai by Rachita Gulati Senior Research Fellow, Punjab School of Economics, Guru Nana Dev University, Amritsar-43005, Punjab, India. E-mail: rachita302@yahoo.co.in

Estimation of technical, pure technical and scale efficiencies of Indian bans: An analysis from cross-sectional perspective Rachita Gulati Senior Research Fellow, Punjab School of Economics, Guru Nana Dev University, Amritsar E-mail: rachita302@yahoo.co.in Abstract: This paper endeavours to measure the extent of technical, pure technical and scale efficiencies of Indian domestic baning industry using the non-parametric technique of data envelopment analysis. The empirical results show that only 9 of the 5 domestic bans operating in the financial year 2006/07 are found to be efficient and, thus, define the efficient frontier of the Indian domestic baning industry, with the TE scores range from 0.505 to, with an average of 0.792. We note that managerial inefficiency is the main source of overall technical inefficiency in Indian domestic baning industry. The new private sector bans dominate in the formation of the efficient frontier. However, the efficiency differences between public and private sector bans are not statistically significant. However, there exists significant differences between large and medium bans appear with regard to scale efficiency. The results pertaining to Tobit analysis reveal that the exposure to off-balance sheet activities and profitability are the most influential determinants of the technical efficiency. Keywords: Data envelopment analysis (DEA), Tobit analysis, Indian bans, Returns-to-scale. Introduction It has been well documented in the literature that the efficiency of baning system is germane to the performance of the entire economy because only an efficient system guarantees the smooth functioning of nation s payment system and effective implementation of the monetary policy. Rajan and Zingales (998) asserted that a sound baning system serves as an important channel for achieving economic growth through the mobilization of financial savings, putting them to productive use, and transforming various riss. The efficiency of baning system also bears direct implications for social welfare. Society benefits when a country s baning system becomes more efficient, offering more services at a lower cost (Valverde et al., 2003). Owing to aforementioned socio-economic implications of baning efficiency, the analyses of relative efficiency of bans gained a lot of popularity among the policy maers, ban managers, ban investors and academicians. The information obtained from baning efficiency analyses can be used either: (i) to inform government policy by assessing the effects of deregulation, mergers, or maret structure on efficiency; (ii) to address research issues by describing the efficiency of an industry, raning its firms, or checing how measured efficiency may be related to the different efficiency techniques employed; or (iii) to improve managerial performance by identifying best practices and worst practices associated with high and low measured efficiency, respectively, and encouraging the former practices and while discouraging latter (Berger and Humphrey, 997). The baning industry has undergone significant transformation all over the world since the early 980s under the impact of technological advances, deregulation, and globalization (Reserve Ban of India, 2008). The Indian baning sector has not remained insulated from the global trends, and deregulated its baning sector in 992 by introducing a series of baning reforms measures lie dismantling of administrated interest rate structure, reduction in statutory pre-emptions in the form of cash reserve ratio (CRR) and statutory liquidity ratio (SLR), introduction of prudential norms in the line with the international best practices, and liberal entry 2

of de novo domestic private and foreign bans, etc. Consequently, the operating environment for the bans has changed significantly, and they are faced with increased competitive pressures and changing customer demands. This has engendered the bans to bring changes in their business strategies, so as to eep their survival intact and maintain a sustainable level of growth. Further, these pressures forced the bans to reduce operating costs while maintaining or improving the quality of their services. As the maretplace continues to evolve at a rapid pace, it has become imperative for bans to remain efficient in production process so that they can withstand the forces of competition and thrive in a changing environment. Against this bacdrop, we have carried out this study with the primary objective to measure the magnitude of the technical efficiency in 5 domestic bans operating in India in the financial year 2006/07. Also, we intend to explore the most influential factors causing inter-ban variations in technical efficiency. To sum up, the aim of this paper is four-fold: i) to obtain a measure of overall technical, pure technical, and scale efficiencies for individual bans; ii) to provide a complete raning to Indian domestic bans on the basis of super-efficiency scores; iii) to examine whether ownership and size matters in Indian domestic baning industry; and iv) to explain the factors determining the OTE of Indian domestic baning industry. To achieve the underlined objectives of the study, we used the non-parametric frontier approach, data envelopment analysis (DEA), to measure the extent of OTE and its components, and to determine the nature of RTS in individual bans using a recent cross-section sample of 5 bans. Further, we made use of Tobit analysis to explain the factors affecting the OTE of Indian domestic bans. The paper unfolds as follows. Section 2 provides a relevant literature review with special reference to Indian baning industry. Section 3 outlines CCR and BCC models for obtaining efficiency measures corresponding to constant returns-to-scale (CRS) and variable returns-toscale (VRS) assumptions, respectively. The description of the data and the specification of input and output variables are reported in the Section 4. Section 5 presents the empirical results and discussion. The relevant conclusions and directions for future research are provided in the Section 6. 2. Relevant literature review In recent years, there has been a proliferation of academic studies on baning efficiency which are primarily confined to the baning system of US and other well-developed European countries (see Berger et al., 993; Berger and Humphrey, 997; Berger and Mester, 997; Ashton and Hardwic, 2000; Casu and Molyneux, 200; Mohtar et al., 2006 for an extensive review of literature on the subject matter). In their extensive international literature survey, Berger and Humphrey (997) pointed out that out of 30 efficiency analyses of financial institutions covering 2 countries, only about 5 percent examined the baning sectors of developing countries. In Indian context, Keshari and Paul (994) were perhaps the first to estimate the efficiency of bans using the frontier methodology. Since then, some notable attempts have been made by the researchers to analyze: (i) the impact of deregulation and liberalization measures on the efficiency and productivity of Indian bans; (ii) the efficiency differences among bans across different ownership groups; and iii) the efficiency differences among public sector bans. Sweeping changes in the Indian baning system which occurred with the advent of the era of deregulation and baning reforms in early 990s motivated the researchers to scrutinize whether the reform measures brought an ascent in efficiency levels of bans across different 3

ownership groups or not. The study of Bhattacharyya et al. (997a) divulged that deregulation has led to an improvement in the overall performance of Indian commercial bans. Bhattacharyya et al. (997b) also reported a positive impact of deregulation on the total factor productivity (TFP) growth of Indian public sector bans. Ataullah et al. (2004) reported that overall technical efficiency of the baning industry of India and Paistan improved following the financial liberalization. Ram Mohan and Ray (2004) found an improvement in the revenue efficiency of Indian bans. Also, they noticed a convergence in performance between public and private sector bans in the post-reforms era. Shanmugam and Das (2004) observed that during deregulation period, the Indian baning industry showed a progress in terms of efficiency of raising non-interest income, investments and credits. Reddy (2004, 2005) noted an ascent in the overall technical efficiency of Indian bans during the period of deregulation. Das et al. (2005) found that the efficiency of Indian bans, in general, and of bigger bans, in particular, has improved during the post-reforms period. The methodology and findings of the study of Mahesh and Rajeev (2006) is completely similar to that of Shanmugam and Das (2004). Chatterjee (2006) noticed a declining trend in the cost inefficiency of the bans during the post-reforms era. Sensarma (2006) noted that deregulation in Indian baning industry (especially public sector bans) achieved the aim of reduction in intermediation costs and improving TFP. Zhao et al. (2007) noted that, after an initial adjustment phase, the Indian baning industry experienced sustained productivity growth, driven mainly by technological progress. On comparing the effect of deregulation on the productivity growth of bans in Indian sub-continent (including India, Paistan and Bangladesh), Jaffry et al.(2007) concluded that technical efficiency both increased and converged across the Indian sub-continent in response to reforms. Rezvanian et al. (2008) reported an ascent in cost efficiency in all ownership groups and industry as a whole. Further, the observed increase in cost efficiency has taen place due to its allocative efficiency improvement rather than technical efficiency gains. Ketar and Ketar (2008) noted that the efficiency scores of all bans, in general, have improved regardless of their ownership during the period of reforms. Further, the nationalized bans have registered the strongest gains. These gains in efficiency have shown an improvement in ban profitability. Reserve Ban of India (2008) found that the efficiency has improved across all ban groups during the study period and most of the observed efficiency gains have emanated after few years of reforms i.e., from 997/98 onwards. Sahoo and Tone (2009) found that competition created after financial sector reforms generated high efficiency growth and reduced excess capacity in Indian baning sector. Though aforementioned studies reflect a positive effect of deregulation on the efficiency and productivity of Indian baning sector, there are also a few studies which reported an adverse effect of deregulatory environment on the performance of Indian bans. For example, Kumbhaar and Sarar (2003) concluded that a significant TFP growth has not been observed in Indian baning sector during the deregulatory regime. Galagedera and Edirisuriya (2005) observed that deregulation has brought no significant growth in the productivity of Indian bans. Further, public sector bans have not responded well to the deregulatory measures. Das and Ghosh (2006) found that the period after liberalization did not witness any significant increase in number of efficient bans and some bans have high degree of inefficiency during the period of liberalization. Sensarma (2005, 2008) pointed out that the profit efficiency of Indian bans has shown a declining trend during the period of deregulation. In the literature on Indian baning, there are also a few studies which have been carried with the main objective to examine the impact of ownership on the efficiency of bans. Keshari and Paul (994) observed that foreign bans as a group have been found to be less efficient than 4

domestic bans and the standard deviation of technical efficiency of foreign bans was slightly higher than that of domestic bans. However, the efficiency differences were not significant. A few researchers lie Bhattacharyya et al. (997a), Muherjee et al. (2002), Sathye (2003), Ram Mohan and Ray (2004), Das and Ghosh (2006), Mahesh and Rajeev (2009) concluded that the bans with public ownership are more efficient than their private counterparts, while others lie Khatri (2004), Charabarti and Chawla (2005), Chatterjee and Sinha (2006), Mittal and Dhingra (2007) concluded that private sector bans are relatively best-performers. Das (997b) and Reserve Ban of India (2008) found no significant differences in any of the efficiency measures between public and private sector bans. Srivastava and Jain (2006) and Debasish (2006) found that foreign owned bans are, on an average, more efficient than domestic bans. Singh et al. (2008) found that foreign bans are more efficient and showed an efficiency improvement during the study period while nationalized bans observed a fall in efficiency. Gupta et al. (2008) noted that SBI and its associates have the highest efficiency, followed by private sector bans, and the other nationalised bans. A few studies also appear in the literature which exclusively concentrated on the efficiency of public sector bans (PSBs). Noulas and Ketar (996) analyzed the technical and scale efficiencies of 8 PSBs and found that majority of the bans were operating under increasing returns-to-scale. Das (997a, 2000) found that the bans belonging to State Ban of India (SBI) group are more efficient than nationalized bans. Main source of inefficiency was technical in nature, rather than allocative. However, PSBs have improved their allocative efficiency in the post-liberalization period. Saha and Ravisanar (2000) noted that the PSBs have, in general, improved their efficiency scores over the period 99/92 to 994/95. Nath et al. (200) generated 5 strategic groups for 27 PSBs using the techniques of DEA and Co-plot. They noted that there is a positive association between efficiency and profitability, and poor performing bans are plagued with over-staffing, low productivity and inefficient training facilities. Kumar and Verma (2003) observed that technical efficiency of PSBs is positively related to higher profitability, larger branch networ and higher staff productivity. Muherjee et al. (2003) found that PSBs delivering better services have better transformation of resource to performance using superior service delivery as the medium. Nandy (2007) found that Corporation Ban and Indian Overseas Ban are the star performers among PSBs. Sanjeev (2007) found that there is no conclusive relationship between the efficiency and size of public sector bans. Kumar (2008) analyzed the efficiency-profitability relationship in individual PSBs and found that Andhra Ban and Corporation Ban are ideal benchmars on both efficiency and profitability dimensions. Kumar and Gulati (2008) noted that the exposure to off-balance sheet activities, staff productivity, maret share and size are the major determinants of the technical efficiency of PSBs. Tandon (2008) analyzed the efficiency of 9 PSBs during the period 2003-2006 and found that Corporation Ban is consistently best-performer. Das et al. (2009) noticed a considerable variation in the average levels of labour-use efficiency of individual branches of a large public sector bans. Kumar and Gulati (2009) found not only an ascent in technical efficiency of the PSBs during the post-reforms years, but also noticed the presence of convergence phenomenon in the Indian public sector baning industry. From the deep analysis of existing literature on Indian baning sector, we can draw following inferences. First, an overwhelming majority of studies portraits a positive impact of deregulatory policies on the efficiency and productivity of Indian bans. Second, the ownership effect on the efficiency of Indian bans is inconclusive. It is significant to note that the existing studies particularly aiming at studying the efficiency differences between domestic and foreign 5

bans, assume a common technology, and therefore quantify the relative efficiency of both domestic and foreign bans using a common efficient frontier. However, this assumption of common frontier is economically irrational and practicably implausible since both foreign and domestic bans follow different technology and baning practices. Third, the average technical inefficiency across PSBs ranges between 20 and 30 percent. 3 Methodology 3. Data envelopment analysis As already pointed out, the technique of data envelopment analysis (DEA) has been used to assess the relative efficiency of Indian domestic bans. DEA generalizes the Farrell s (957) technical efficiency measure to the multiple-inputs and multiple-outputs case. DEA involves the use of linear programming methods to construct a non-parametric piecewise surface (frontier) over the data. Efficiency measures are then calculated relative to this surface. Comprehensive review of the methodology is presented in Seiford and Thrall (990), Charnes et al. (994), Seiford (996), Zhu (2003), Ray (2004) and Cooper et al. (2007). DEA optimizes each individual observation with the objective of calculating a discrete piecewise linear frontier determined by the set of Pareto-efficient decision maing units (DMUs). Using this frontier, DEA computes a maximal performance measure for each DMU relative to that of all other DMUs. The only restriction is that each DMU lies on the efficient (extremal) frontier or be enveloped within the frontier. The DMUs that lie on the frontier are the best practice units and retain a value of ; those enveloped by the extremal surface are scaled against a convex combination of the DMUs on the frontier facet closest to it and have values somewhere between 0 and. Several different mathematical programming DEA models have been proposed in the literature. Essentially, these models see to establish which of n DMUs determine the envelopment surface or best practice frontier or efficient frontier. The geometry of this surface is prescribed by the specific DEA model employed. In the present study, we use the CCR (named after its developers Charnes, Cooper and Rhodes, 978) and BCC (named after its developers Baner, Charnes and Cooper, 984) models to obtain efficiency measures corresponding to the assumptions of CRS and VRS, respectively. The efficiency measures obtained from CCR model are popularly nown as overall technical efficiency (OTE) scores and are confounded by scale efficiencies. The efficiency measures obtained from BCC model are popularly nown as pure technical efficiency (PTE) scores and devoid of scale efficiency effects. Scale efficiency (SE) for each DMU can be obtained by a ratio of OTE score to PTE score (i.e., SE=OTE/PTE). 3.2 CCR model To illustrate CCR model, consider a set of decision maing units (DMUs) j=,2,..., n, utilizing m s quantities of inputs X R + to produce quantities of outputsy R +. We can denote x ij the amount of the ith input used by the DMU j and y rj the amount of the rth output produced by the DMU j. Assuming constant returns-to-scale (CRS), strong disposability of inputs and outputs, and convexity of the production possibility set, the technical efficiency score for the DMU (denoted by TE ) can be obtained by solving following model (Charnes et al., 978): 6

() i) min + θ,λ,s i,sr subject to m s TECRS = θ ε si s + i= r = + r n + ii) λ j yrj sr = yr r=,2,..., s j= n iii) λ jxij + si = θ xi i=,2,..., m j= + iv) s i, sr 0 v) λ j 0 j=,2,..., n The solution to model () is interpreted as the largest contraction in inputs of DMU that can be carried out, given that DMU will stay within the reference technology. The restrictions ii) and iii) form the convex reference technology. The restriction iv) restricts the input slac ( s ) and output slac ( s + r ) variables to be non-negative. The restriction v) limits the intensity variables to be non-negative. Parameter ε is a non-archimedean infinitesimal. Since the model measures the efficiency of single DMU (i.e., DMU ), it needs to be solved n times to obtain efficiency score of each DMU in the sample. The optimal value θ reflects the OTE score of DMU. OTE measures inefficiencies due to the input/output configuration and as well as the size of operations (Aviran, 2006). This efficiency score is within a range from zero to + one, 0< θ, with a high score implying a higher efficiency. If θ = and si = sr = 0 then DMU is Pareto-efficient. It is worth mentioning here that the model () is an input-oriented model since the objective is to utilize minimum level of inputs with the same level of production. 3.3 BCC model The CCR model detailed above provide the input-oriented constant returns-to-scale(crs) envelopment surface, and a measure of overall technical efficiency( θ ).Under the assumption of CRS, any scaled-up or scaled-down versions of the input combinations are also included in the production possibility set. However, the constraint over returns-to-scale may be relaxed to allow units to be compared given their scale of operations. To allow returns-to-scale to be variable (i.e., constant, increasing or decreasing), Baner, Charnes and Cooper (984) added the convexity constraint n λ = to the Model (). Note that the convexity constraint j= j n λ =, essentially ensures that an inefficient DMU is only benchmared against DMUs of a similar size. The mathematical form of BCC model is as follows: j= j i 7

(2) i) min TEVRS = π ε s + s + θ,λ,s,s subject to n j= j= j= m s + i r i= r= ii) λ y s = y r=, 2,..., s n iii) λ x + s = θ x i=, 2,..., m n iv) λ = v) s, s 0 i r + j rj r r j + i r j ij i i vi) λ 0 j=, 2,..., n j The optimal value of the π (i.e., π ) represents pure technical efficiency which is a measure of efficiency without scale efficiency. We should also note that if a DMU is characterized as efficient in the CCR model, it will also be characterized as efficient with the BCC model. However, the converse is not necessarily true. 3.4 Scale efficiency and returns-to-scale An optimal value of scale efficiency (SE) measure for DMU as denoted by. obtained as: µ = θ π Since π θ it follows that fully scale efficient. If µ. If µ can be µ = then the DMU is µ <, the DMU is scale inefficient. There are two possible reasons for scale inefficiency. The DMU could be operating under increasing returns-to-scale (IRS) and, therefore, be of sub-optimal scale. Alternatively, the DMU could be operating under decreasing returns-to-scale (DRS) and, therefore, be of supra-optimal scale. To determine whether the DMU is operating in an area of increasing or decreasing returns-to-scale, we run an additional DEA problem with non-increasing returns-to-scale (NIRS) imposed. This is done by altering the BCC model by substituting the n λ = restriction with λ to provide: j= j n j= j 8

(3) j= j= j= m s + ( i r ) i) min TE = δ ε s + s + NIRS δ,λ,s,s i= r= subject to n ii) λ y s = y r=,2,..., s n iii) λ x + s = δ x i=, 2,..., m n iv) λ v) s, s 0 Note that the constraint i r + j rj r r j ij i i j + i r vi) λ 0 j=,2,..., n j n λ ensures that th DMU will not be benchmared j= j against DMUs which are substantially larger than it, but may be compared with DMUs smaller than it. If µ < and θ = δ then scale inefficiency is due to IRS and the DMU is of sub-optimal size. On the other hand, if µ < and θ < δ then scale inefficiency is due to DRS and the DMU is of supra-optimal size. Corresponding to the three measures of efficiency defined above are three measures of inefficiency defined in the obvious way, namely, θ, π and µ. In fact, θ gives the necessary reduction in all inputs of DMU to be rated as fully efficient. Further, overall technical inefficiency, inefficiency, π θ, can be thought of as being attributable to pure technical, and scale inefficiency, µ, and the former sometimes referred to as controllable, managerial or X-inefficiency (Alexander and Jaforullah, 2005). 3.5 Andersen and Petersen s Super-efficiency model It is significant to note that all the efficient DMUs have OTE scores equal to in the CCR model. Therefore, it is impossible to ran or differentiate the efficient DMUs with the CCR model. However, the ability to ran or differentiate the efficient DMUs is of both theoretical and practical importance. Theoretically, the inability to differentiate the efficient DMUs creates a spied distribution at efficiency scores of. This poses analytic difficulties to any post-dea statistical inference analysis. In practice, further discrimination across the efficient DMUs is also desirable to identify ace performers. For getting strict raning among the efficient DMUs, Andersen and Petersen (993) proposed the super-efficiency DEA model. The core idea of superefficiency DEA model is to exclude the DMU under evaluation from the reference set. The super-efficiency score for efficient DMU can, in principle, tae any value greater than or equal to. This procedure maes the raning of efficient DMUs possible (i.e., the higher the superefficiency score implies higher ran). However, the inefficient units which are not on the efficient frontier, and with an initial DEA score of less than, would find their relative efficiency score unaffected by their exclusion from the reference set of DMUs. In the super-efficiency DEA model, when the linear program (LP) is run for calculating the efficiency score of DMU, the DMU cannot form part of its reference frontier and hence, if 9

it was a fully-efficient unit in the original standard DEA model (lie CCR model in the present study) it may now have efficiency score greater than. This LP is required to be run for each of the n DMUs in the sample, and in each of these LPs, the reference set involves n- DMUs. In particular, Andersen and Petersen s model for estimating super-efficiency score for DMU (denoted byte (4),super CRS ) can be outlined as below: super j=, j j=, j,super CRS super super j ij i θ i m s + ( i r ) i) min TE = θ ε s + s + i= r= θ,λ,s,s subject to n ii) λ y s = y r=, 2,..., s n iii) λ x + s = x i=, 2,..., m i iv) s, s i r + r + j rj r r 0 v) λ ( j ) 0 j=,2,..., n j 3.6 Tobit analysis The standard Tobit model can be defined as follows for ith observation (ban) is as follows: y T i = β xi + ε i i i if i y = y y > y i = 0, o th erw ise 0, an d 2 whereε i ~ N(0, σ ), x i and β are vectors of explanatory variables and unnown parameters, respectively. T denotes the matrix transpose operator. y i is a latent variable and y i is the dependent variable. The lielihood function (L) is maximized to solveβ and σ based on 5 observations (bans) of y i and x i is where, Fi = 2 T t i β x / σ ( 2π) / 2 e 2 L= ( F) 2 i e σ / 2 yi= 0 yi> 0 2 dt 2 ( πσ ) 2( y T i β xi) The first product is over the observations for which the industrial groups are 00 percent efficient (y = 0) and the second product is over the observations for which industrial groups are T inefficient (y > 0). F is the distribution function of the standard normal evaluated at β x / i i σ. It is possible to estimate the unnown parameter vector β in the Tobit model in several ways. 4. Data and specification of inputs and outputs In the baning literature, there is a considerable disagreement among researchers about what constitute inputs and outputs of baning industry (Casu, 2002; Sathye, 2003). Two different approaches appear in the literature regarding the measurement of inputs and outputs of a ban. 2 0

These approaches are the production approach and intermediation approach (Humphrey, 985). The intermediation approach views the bans as using deposits together with purchased inputs to produce various categories of ban assets. Outputs are measured in monetary values and total costs include all operating and interest expenses (see Sealey and Lindley, 977 for a discussion). In contrast, the production approach view bans as using purchased inputs to produce deposits and various categories of ban assets. Both loans and deposits are, therefore, treated as outputs and measured in terms of the number of accounts. This approach considers only operating costs and excludes the interest expenses paid on deposits since deposits are viewed as outputs. Although the intermediation approach is most commonly used in the empirical studies, neither approach is completely satisfactory, largely because the deposits have both input and output characteristics which are not easily disaggregated empirically. Berger and Humphrey (997) suggested that the intermediation approach is best suited for analyzing ban level efficiency, whereas the production approach is well suited for measuring branch level efficiency. This is because, at the ban level, management will aim to reduce total costs and not just non-interest expenses, while at the branch level a large number of customer service processing tae place and ban funding and investment decisions are mostly not under the control of branches. Also, in practice, the availability of flow data required by the production approach is usually exceptional rather than in common. Therefore, following Berger and Humphrey (997), we have selected a modified version of intermediation approach as opposed to the production approach for selecting input and output variables in the present study. The data on input and output variables have been culled out from two annual publications of Indian Bans Association entitled, Performance Highlights of Public Sector Bans: 2006/07 and Performance Highlights of Private Sector Bans: 2006/07. The study is confined to 5 public and private sector bans operating in the financial year 2006/07 3. In this study, the inputs used for computing various efficiency scores are i) physical capital 4, ii) labour 5, and iii) loanable funds 6. The output vector contains two output variables: i) net-interest income 7, and ii) noninterest income 8. The variable net-interest income connotes net income received by the bans from their traditional activities lie advancing of loans and investments in the government and other approved securities. The output variable non-interest income accounts for income from off-balance sheet items such as commission, exchange and broerage, etc. The inclusion of noninterest income enables us to capture the recent changes in the production of services as Indian bans are increasingly engaging in non-traditional baning activities. As pointed out by Siems and Clar (997), the failure to incorporate these types of activities may seriously understate ban output and this is liely to have statistical and economic effects on estimated efficiency. It is worth noting here that the choice of output variables is consistent with the managerial objectives that are being pursued by the Indian bans. In the post-reforms years, intense competition in the Indian baning sector has forced the bans to reduce all the input costs to the minimum and to earn maximum revenue with less of less inputs. Further, the inclusion of deposits and loans in the output vector as reported in the studies of Muherjee et al. (2002) and Charabarti and Chawla (2005) is not in consonance of policy objectives of the Indian bans and, thus, seems irrational in the efficiency analysis of Indian bans that confined to the postreforms period. In this context, Ram Mohan and Ray (2004) rightly remared that: Using deposits and loans as outputs would have been appropriate in the nationalized era when maximizing these was indeed the objective of a ban but they are, perhaps, less appropriate in the reforms era. Bans are not simply maximizing deposits and loans; they are in the business of maximizing profits. If inputs are treated as pre-determined, this amounts to maximizing revenue.

5. Empirical results In this section, we provide and discuss the contents of OTE, PTE and SE scores that are obtained by executing the two most generic DEA models, namely, CCR and BCC models. Further, the results pertaining to RTS are also provided herewith. The results of the DEA modeling are derived from the computer program DEA Excel Solver developed by Zhu (2003). Table presents OTE, PTE and SE scores along with nature of RTS for individual bans. The subsequent discussion is based on the summary tables prepared from Table. The perusal of table gives that out of 5 sample bans, only 9 bans have been found to be overall technically efficient with OTE score equal to. These efficient bans together define the efficient frontier of Indian domestic baning industry and, thus, form the reference set for inefficient bans. The level of overall technical inefficiency (OTIE) 9 in the remaining 42 inefficient bans can be gauged as the radial distance from this frontier. The frontier bans are State Ban of Bianer and Jaipur, Andhra Ban, Nainital Ban, Tamilnad Mercantile Ban, Centurion Ban of Punjab, HDFC Ban, ICICI Ban, Kota Mahindra Ban, and Yes Ban. Note that a total of 5 out of 9 overall technically efficient bans are de nova private sector bans which were established after 996. Thus, the de nova private sector bans armed with state-ofthe-art baning technology and business practices dominate in the formation of efficient frontier for Indian domestic baning industry. It is noteworthy here that the process of resource utilization in the aforementioned frontier bans is functioning well, and featuring no waste of resources. In the spirit of DEA terminology, these bans can be termed as global leaders (or globally efficient bans) and set the idyllic benchmars of best operating practices in the Indian domestic baning industry. Further, the inefficient bans identified in the sample could move towards the efficient frontier by emulating the best practices of these efficient bans. That is, the ultimate destination for all inefficient bans in their drive to achieve high level of performance is to follow the input-output combinations that are being used by the global leaders. 2

Table OTE, PTE, SE and returns-to-scale in Indian domestic bans Ban Public Sector Bans OTE PTE SE RTS Ban code code Private Sector Bans OTE PTE SE RTS B State Ban of India 0.892.000 0.892 DRS B29 City Union Ban 0.770 0.829 0.929 IRS B2 State Ban of Bianer and Jaipur.000.000.000 CRS B30 Development Credit Ban 0.895 0.960 0.932 IRS B3 State Ban of Hyderabad 0.924 0.926 0.998 DRS B3 ING Vysya Ban 0.639 0.653 0.979 IRS B4 State Ban of Indore 0.88 0.888 0.993 IRS B32 Karnataa Ban 0.80 0.804 0.996 IRS B5 State Ban of Mysore 0.948 0.968 0.979 DRS B33 Nainital Ban.000.000.000 CRS B6 State Ban of Patiala 0.935 0.939 0.995 DRS B34 SBI Commercial & Int. Ban 0.653.000 0.653 IRS B7 State Ban of Saurashtra 0.540 0.542 0.997 IRS B35 Tamilnad Mercantile Ban.000.000.000 CRS B8 State Ban of Travancore 0.902 0.980 0.920 DRS B36 Ban of Rajasthan 0.567 0.608 0.934 IRS B9 Allahabad Ban 0.56 0.563 0.997 IRS B37 Catholic Syrian Ban 0.672 0.70 0.958 IRS B0 Andhra Ban.000.000.000 CRS B38 Dhanalashmi Ban 0.600 0.656 0.95 IRS B Ban of Baroda 0.690 0.775 0.89 DRS B39 Federal Ban 0.873 0.874 0.998 DRS B2 Ban of India 0.838 0.994 0.843 DRS B40 Jammu & Kashmir Ban 0.797 0.83 0.959 DRS B3 Ban of Maharashtra 0.732 0.82 0.892 DRS B4 Karur Vysya Ban 0.74 0.756 0.980 IRS B4 Canara Ban 0.536 0.566 0.947 DRS B42 Lashmi Vilas Ban 0.625 0.686 0.90 IRS B5 Central Ban of India 0.600 0.678 0.885 DRS B43 Ratnaar Ban 0.80.000 0.80 IRS B6 Corporation Ban 0.988.000 0.988 DRS B44 South Indian Ban 0.706 0.77 0.984 DRS B7 Dena Ban 0.638 0.645 0.988 IRS B45 Centurion Ban of Punjab.000.000.000 CRS B8 Indian Ban 0.79 0.794 0.996 DRS B46 HDFC Ban.000.000.000 CRS B9 Indian Overseas Ban 0.89 0.948 0.864 DRS B47 ICICI Ban.000.000.000 CRS B20 Oriental Ban of Commerce 0.874 0.882 0.99 DRS B48 IndusInd Ban 0.632 0.650 0.972 IRS B2 Punjab & Sind Ban 0.759 0.76 0.997 IRS B49 Kota Mahindra Ban.000.000.000 CRS B22 Punjab National Ban 0.88.000 0.88 DRS B50 UTI Ban 0.936 0.938 0.998 IRS B23 Sydicate Ban 0.59 0.68 0.956 DRS B5 Yes Ban.000.000.000 CRS B24 UCO Ban 0.505 0.552 0.96 DRS B25 Union Ban of India 0.692 0.746 0.927 DRS B26 United Ban of India 0.60 0.604 0.995 IRS B27 Vijaya Ban 0.849 0.896 0.948 DRS B28 IDBI Ban 0.772 0.780 0.989 IRS Note: RTS= Returns-to-scale, IRS=Increasing returns-to-scale, DRS=Decreasing returns-to-scale, and CRS= Constant returns-to-scale Source: Authors calculations 3

Table 2: Frequency distribution and descriptive statistics of OTE, PTE and SE scores Efficiency Scores OTE PTE SE E < 0.5 0 (0.00) 0 (0.00) 0 (0.00) 0.5 E < 0.6 6 (.77) 4 (7.84) 0 (0.00) 0.6 E < 0.7 (2.57) 9 (7.65) (.96) 0.7 E < 0.8 8 (5.69) 8 (5.69) 0 (0.00) 0.8 E < 0.9 (2.57) 8 (5.69) 8 (5.68) 0.9 E <.0 6 (.77) 8 (5.69) 33 (64.7) E=.0 9 (7.6) 4 (27.45) 9 (7.65) Descriptive Statistics No. of Bans 5 5 5 Mean 0.792 0.834 0.95 Median 0.80 0.874 0.980 Standard Deviation 0.55 0.55 0.066 Q 0.646 0.694 0.924 Q 3 0.930.000 0.997 Minimum 0.505 0.542 0.653 Maximum.000.000.000 Notes: (i) Q =First Quartile and Q 3 =Third Quartile; and (ii) Figures in parenthesis are the percentage of bans. Source: Authors calculations Table 2 provides the frequency distribution of OTE, PTE and SE scores and their descriptive statistics. From the table, we observe that OTE scores range between 0.505 and, and their mean and standard deviation (SD) are 0.792 and 0.55, respectively. Thus, the average level of OTIE in Indian domestic baning industry is to the tune of about 2.8 percent. It can, therefore, be concluded that the same level of outputs in Indian domestic baning sector could be produced with 2.8 percent lesser inputs. Further, we note the presence of significant variations in OTIE at the level of individual bans. The highest and lowest levels of OTIE have been noted for UCO Ban (49.5 percent) and Corporation Ban (.2 percent), respectively (see Table for OTE scores of these bans). The analysis of frequency distribution of OTE scores reveals that about 49 percent of bans have efficiency score below 0.8 and, thus, have OTIE more than 20 percent. As noted above, OTE can be decomposed into two mutually exclusive and non-additive components, namely, pure technical efficiency (PTE) and scale efficiency (SE). It is significant to note that lie OTE measure, the PTE measure also indicates the underutilization of inputs. However, in contrast to the OTE measure, the PTE measure is devoid of scale effects. Table 2 also provides the frequency distribution of PTE scores along with their relevant descriptive statistics. The mean value of PTE scores has been observed to be 0.834 (with SD of 0.55), and PTE scores range from the lowest figure of 0.542 to the highest of. Thus, the extent of pure technical inefficiency (PTIE) 0 in Indian domestic baning industry has been observed to be 6.6 percent. The results delineate that 6.6 percentage points of 2.8 percent of OTIE identified above in the Indian domestic baning industry is due to inappropriate management practices that are being followed by bans managers in organizing inputs in baning operations. The remaining part of OTIE is due to the bans operating at sub-optimal scale size. This implies that in Indian domestic baning industry, PTIE is a more dominant source of OTIE, and scale inefficiency (SIE) is a relatively diminutive one. Further, 4 bans have been identified as relatively efficient under VRS assumption since they have attained PTE score equal to. Out of these 4 bans, 9 bans were also relatively efficient under CRS assumption with OTE score 4

equal to. Thus, in only 5 bans, the OTIE is caused entirely by SIE rather than PTIE. In other words, the OTIE in these bans is completely due to inappropriate choice of the scale size instead of managerial incapability to organize the resources in the production process. These 5 bans are State Ban of India, Corporation Ban, Punjab National Ban, SBI Commercial & Int. Ban, and Ratnaar Ban. We further note that in 40.9 percent bans, the extent of PTIE is more than 20 percent. As mentioned earlier, SE score for each ban can be obtained by taing a ratio of OTE score to PTE score. The value of SE equal to implies that the ban is operating at most productive scale size (MPSS) which corresponds to constant returns-to-scale. At MPSS, the ban operates at minimum point of its long-run average cost curve. Further, SE< indicates that the ban is experiencing OTIE because it is not operating at its optimal scale size. An inspection of Table 2 reveals that mean SE for Indian domestic baning industry as a whole is quite high being 0.95 (with SD equal to 0.066), and SE scores range from a minimum of 0.653 to maximum of. The connotation of this finding is that average level of SIE in the Indian domestic baning sector is to the tune of about 4.9 percent. This finding reiterates our earlier findings that SIE is a scant source of OTIE relative to that of PTIE in Indian domestic baning industry. Further, only 9 bans attained SE score equal to and are, thus, operating at most productive scale size (MPSS). The remaining 42 bans are operating with some degree of SIE and have either DRS or IRS. In addition, the majority of bans are operating with scale efficiency above 80 percent. 5. Discrimination of efficient bans: super-efficiency DEA model The Anderson and Peterson s super-efficiency scores obtained for the efficient bans and their rans are reported in Table 3. We note that among the efficient bans, ICICI Ban dominates the whole sample with the super-efficiency score equal to.66 and, thus, raned at the top position among the 5 bans under consideration. Another private sector ban, Yes Ban occupied the second place with super-efficiency score equal to.43. Further, HDFC Ban, Nainital Ban, Centurion Ban of Punjab have occupied third, fourth and fifth place, respectively. Two more private sector bans, namely, Tamilnad Mercantile Ban and Kota Mahindra Ban acquired seventh and ninth place, respectively, among the efficient bans of Indian domestic baning industry. However, only two public sector bans, namely, State Ban of Bianer and Jaipur, and Andhra Ban attained the status of efficient bans and raned at sixth and eighth positions, respectively. Table 3 Andersen and Petersen s super-efficiency scores and rans of efficient bans Ban Andersen and Petersen s super-efficiency scores Ran ICICI Ban.660 Yes Ban.43 2 HDFC Ban.288 3 Nainital Ban.225 4 Centurian Ban of Punjab.20 5 State Ban of Bianer and Jaipur.090 6 Tamilnad Mercantile Ban.083 7 Andhra Ban.034 8 Kota Mahindra Ban.02 9 Source: Authors calculations 5

5.2 Discrimination of inefficient bans In order to get a deep insight into the behaviour of inefficient bans, we made an attempt to classify 42 inefficient bans into four broad categories. The values for first quartile( Q ), median, and third quartile( Q 3) of OTE scores have been selected as three cut-off points to discriminate the inefficient bans. Table 4 provides the classification of inefficient bans into four distinct categories. Table 4 Discrimination of Inefficient Bans Category I (Below Q ) Category II ( Q <OTE<Median) Category III (Median<OTE< Q 3 ) Category IV ( Q 3 <OTE<) UCO Ban (5) SBI Commercial & Int. Ban(38) Ratnaar Ban (25) State Ban of Patiala (3) Canara Ban (50) Catholic Syrian Ban (37) Punjab National Ban (24) UTI Ban (2) State Ban of Saurashtra (49) Ban of Baroda (36) Indian Overseas Ban (23) State Ban of Mysore () Allahabad Ban (48) Union Ban of India (35) Ban of India (22) Corporation Ban (0) Ban of Rajasthan (47) South Indian Ban (34) Vijaya Ban (2) Sydicate Ban (46) Ban of Maharashtra (33) Oriental Ban of Commerce (20) Central Ban of India (45) Karur Vysya Ban (32) Federal Ban (9) Dhanalashmi Ban (44) Punjab & Sind Ban (3) State Ban of Indore (8) United Ban of India (43) City Union Ban (30) State Ban of India (7) Lashmi Vilas Ban (42) IDBI Ban (29) Development Credit Ban (6) IndusInd Ban (4) Indian Ban (28) State Ban of Travancore (5) Dena Ban (40) Jammu & Kashmir Ban (27) State Ban of Hyderabad (4) ING Vysya Ban (39) Karnataa Ban (26) Note: The figures in parentheses are respective rans of inefficient bans. Source: Authors elaboration Some discussion on the bans in the categories I and IV is warranted here. This is worth mentioning here that the bans in category IV are operating with a high level of OTE and, thus, can be categorized as marginally inefficient bans. These bans can attain the status of globally efficient bans by bringing little improvement in their resource allocation process. Putting it differently, we can say that although these bans are not fully technically efficient yet they are the perspective candidates for the status of global leaders because of their vitality in the terms of input utilization. To achieve high level of total factor productivity (TFP) growth, these bans need to rely more upon the technological change because the resource utilization process of these bans is up to the mar and, thus, efficiency change would be negligible in these bans and would not contribute much to TFP growth. On the other hand, the bans in category I are the worst performers in the sample. These bans need to concentrate more upon minimizing the waste of resources given the existing technology rather than the deepening of technology so as to achieve high level of TFP growth in the future 2. 5.3 Returns-to-scale One of the most significant features of DEA is its capacity to determine whether a DMU is operating in the region of CRS, IRS, or DRS. A DMU exhibiting CRS have optimum or most productive scale size (MPSS), and operates at flatter portion of long-run average cost curve. On the other hand, a DMU exhibits DRS when a percentage increase in inputs produces a less than proportional expansion of outputs. The DMUs experiencing DRS lie above the optimal scale of operations (i.e., at the rising portion of long-run average cost curve) and would improve their efficiency by downsizing their scale of operations (e.g., by splitting into two or more production 6

units that operate under CRS). Further, a DMU exhibits IRS when a percentage increase in inputs produces a more than proportional expansion of outputs. The DMUs experiencing IRS lies below the optimal scale of operations (i.e., at the declining portion of long-run average cost curve) and would improve their efficiency by expanding the size of their scale of operations. As noted above, the existence of increasing or decreasing returns-to-scale can be identified by the equality or inequality of the efficiency scores under CRS, VRS and NIRS assumptions. Table also provides the nature of RTS for individual bans. We note here that 20 (i.e., 39.2 percent) bans in the sample are operating at below their optimal scale size and, thus, experiencing IRS. These bans have sub-optimal scale size and increase in average productivity in these bans would require an expansion in terms of size. In contrast, 22 (i.e., 43. percent) bans experience DRS. These bans have supra-optimal scale size and downsizing is needed for achieving efficiency gains. Further, only 9 (i.e., 7.6 percent) bans are found to be operating at MPSS and experiencing CRS. 5.4 Ownership and efficiency differences Table 5 provides the descriptive statistics of OTE, PTE and SE scores for both public and private sector bans. It has been observed that mean OTE for 28 PSBs is equal to 0.774, whereas the same for 23 private sector bans is 0.84. This indicates that the private sector bans, on an average, are 4 percent more technically efficient in utilizing inputs than the public sector bans. Further, the variability in OTE has been observed to be almost same in both segments of Indian domestic baning industry. The perusal of the table further gives that, on an average, the extent of managerial efficiency as reflected by PTE score, is more in private sector bans relative to public sector bans. This is manifested from the fact that the values of mean PTE have been observed to be 0.87 and 0.855 for public and private sector bans, respectively. The results further provide that, on an average, both public and private sector bans have almost identical levels of scale efficiency. Table 5 Descriptive statistics of efficiency measures in Indian baning industry by ownership groups and size classes Statistics Public Sector Bans Private Sector Bans Small bans Medium bans Large bans Overall Technical Efficiency (OTE) No. of Bans 28 23 24 3 4 Mean 0.774 0.84 0.793 0.825 0.759 Median 0.805 0.80 0.786 0.849 0.795 Standard Deviation 0.52 0.57 0.56 0.53 0.6 Q 0.629 0.653 0.643 0.685 0.598 Q 3 0.895.000 0.945 0.96 0.878 Minimum 0.505 0.567 0.540 0.56 0.505 Maximum.000.000.000.000.000 Pure Technical Efficiency (PTE) No. of Bans 28 23 24 3 4 Mean 0.87 0.855 0.833 0.846 0.824 Median 0.852 0.874 0.852 0.896 0.83 Standard Deviation 0.6 0.47 0.54 0.55 0.72 Q 0.670 0.70 0.690 0.79 0.663 Q 3 0.97.000.000 0.990.000 Minimum 0.542 0.608 0.542 0.563 0.552 Maximum.000.000.000.000.000 Scale Efficiency (SE) 7

No. of Bans 28 23 24 3 4 Mean 0.950 0.953 0.955 0.975 0.923 Median 0.984 0.980 0.982 0.995 0.922 Standard Deviation 0.054 0.080 0.078 0.035 0.060 Q 0.90 0.933 0.933 0.953 0.879 Q 0.995.000 0.998 0.997 0.989 3 Minimum 0.88 0.653 0.653 0.892 0.88 Maximum.000.000.000.000.000 Note: Q =First Quartile and Q 3 =Third Quartile Source: Authors calculations To test whether the efficiency differences between public and private sector bans are statistically significant or not, we applied four statistical tests, namely, Analysis of Variance (ANOVA), Wilcoxon Mann-Whitney test, Krusal-Wallis test and Kolmogorov-Simrnov test. The ANOVA test is parametric in nature and assumes that the underlying distribution is normal and compares public and private sector bans on the basis of mean efficiency measures. Other tests are non-parametric in nature in which normality assumption is not invoed. The Mann- Whitney test compares the two sample distributions of efficiency on the basis of their central tendency, as measured by the median. The remaining two tests compare the entire structures of the distribution, not just the central tendency. The results pertaining to these tests are presented in Table 6. Table 6 Hypothesis testing: efficiency differences between public and private sector bans Parametric test Non-parametric tests Individual Tests ANOVA test Wilcoxon Mann-Whitney test Krusal-Wallis test Efficiency Measures Kolmogorov-Simrnov test H o Mean Public = Mean Median Private Public = Median Private Distribution Public =Distribution Private OTE 0.482.200.477 0.284 (0.072) (0.262) (0.224) (0.86) PTE.244.2.295 0.23 (0.606) (0.230) (0.255) (0.500) SE 0.982 0.97 0.993 0.233 (0.954) (0.327) (0.39) (0.47) Decision Accept H o Accept H o Accept H o Accept H o Notes: ) The figures in parentheses are the p-values associated with the relative test, and 2) The test statistics for ANOVA, Wilcoxon 2 Mann-Whitney, Krusal Wallis, and Kolmogorov Simrnov Test are F, z, χ and D. Source: Authors calculations As can be seen from the table, the test statistics indicate that for all the efficiency measures, the respective null hypothesis cannot be rejected. This implies that the differences in distribution of efficiency measures between public and private sector bans are not significant. Thus, there are insignificant differences in mean levels of OTE, PTE and SE between public and private sector baning segments of Indian domestic baning industry. Accordingly, a wea ownership effect on the performance of bans exists in the Indian domestic baning industry. This could be attributable to the fact that there has been a change in the orientation of PSBs from social objectives towards an ascent in profitability, particularly given that some of these bans have been listed on the stoc exchange and, thus, a stae of private investors is involved. Another factor that seems to have played a role is that PSBs enjoy a huge first-mover advantage in terms of scale of operations over private sector bans and these advantages perhaps offset any inefficiency that could be ascribed to the government ownership (Ram Mohan, 2005). 8